There are 64 rooms and N players. Each player has a random number of coins up to one million.
- Each player takes one or several pets and gives them their coins.
- The pets are then taken one by one and randomly placed in one of the 64 rooms
- Finally, one of the pets' coins is randomly selected in each room. The owner of the coin wins a price.
What strategy will earn more prices, give all the coins to one pet or share them equally between several pets? Or will the chances be the same?
Assume that random is equal distribution.
I came to this problem while learning about Etherume 2.0 sharding mechanism. My gut tells me that having more pets is more beneficial, but I can't prove it mathematically. Please tell me what the correct answer is.